Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 6x - 1$ and $ BC = 8x - 9$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {6x - 1} = {8x - 9}$ Solve for $x$ $ -2x = -8$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 6({4}) - 1$ $ BC = 8({4}) - 9$ $ AB = 24 - 1$ $ BC = 32 - 9$ $ AB = 23$ $ BC = 23$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {23} + {23}$ $ AC = 46$